Irrational Pi Defrocked

[C1ay]

So, from post #86 above we have:

Well, Robust, you have given us four different values for that radius:* 2.25675833419, 2.25675823838, 2.25 and 2.24873078056.* Why don't you save us all some anguish and tell us which one is the correct one in your opinion?

They are all correct

yet now you claim

There is only one circle with the given area - and there is only one radius describing that area.

You have now directly contradicted yourself. How amusing :)

[Robust]

So, from post #86 above we have:

 

yet now you claim

 

You have now directly contradicted yourself. How amusing :)

 

Amusing to you no doubt, Clay, but this is not Playland. There is only one radius giving the area to any circle. If you will, and considering that the circle is a closed continuum, using your irrational pi give the area to any circle as defined by a whole number or ending decimal. It can be done, but I seriously doubt that you can do it using the irrational pi.

[C1ay]

Amusing to you no doubt, Clay, but this is not Playland. There is only one radius giving the area to any circle. If you will, and considering that the circle is a closed continuum, using your irrational pi give the area to any circle as defined by a whole number or ending decimal. It can be done, but I seriously doubt that you can do it using the irrational pi.

If that is your claim then prove it. It is no one else's burden to prove or disprove your claim. Of course, if you can't prove it then it is only your opinion.

[Robust]

If that is your claim then prove it. It is no one else's burden to prove or disprove your claim. Of course, if you can't prove it then it is only your opinion.

 

OK then, Clay, here's a go at it. For the sake of simplicity, let's consider the circle with a radius of 2.25 and configure using the irrational pi and that of the oldest pi value on record, that of 256/81.

 

1. Irrational Pi: r^2*pi = 15.9043 ad infinitum area;

2. 256/81 Pi: r^2*pi = 16 area finite.

 

It's not just my opinion, Clay....just pure mathematics.

[C1ay]

OK then, Clay, here's a go at it. For the sake of simplicity, let's consider the circle with a radius of 2.25 and configure using the irrational pi and that of the oldest pi value on record, that of 256/81.

 

1. Irrational Pi: r^2*pi = 15.9043 ad infinitum area;

2. 256/81 Pi: r^2*pi = 16 area finite.

 

It's not just my opinion, Clay....just pure mathematics.

Comparing a value of pi that the Egyptians calculated using pebbles and sticks with a value that has evolved from thousands of years of mathematical analysis is not a rigorous proof. But hey, if you want to use a value from 3000 years ago have at it. Do you where a sun dial too?

[Robust]

Comparing a value of pi that the Egyptians calculated using pebbles and sticks with a value that has evolved from thousands of years of mathematical analysis is not a rigorous proof. But hey, if you want to use a value from 3000 years ago have at it. Do you where a sun dial too?

 

Man does not etch frivously etch in stone, Clay. The etching of this pi value is believed by archeologists to have been given in advance knowledge of an earthly cataclysmic event endangering the existence of all lifeform on the planet. I trust you do not believe thst we are the most advanced people to have ever lived on this planet. We are indeed making great strides in the applied sciences. At the academic end of it I think we're still mucking about in the Dark Ages.

[C1ay]

Man does not etch frivously etch in stone, Clay.

No he does not. OTOH, The Egyptians believed the universe and all events that occurred within it were governed by the will of gods. After death, the Egyptians looked forward to continuing their daily lives as an invisible spirit among their descendents on Earth in Egypt, enjoying all the pleasures of life with none of its pain or hardships. This vision is vividly depicted in the sculptures, reliefs, and wall paintings of Egyptian tombs, with the deceased portrayed in the way he or she wished to remain forever, accompanied by images of family and servants. The ancient Egyptians believed that the king was given divine power by the gods to maintain universal order and justice against the forces of chaos and evil. On the strength of his divine nature the king mediated between the gods and humankind. The ancient Egyptians believed in curses and spells. Do you believe this too since you seem to believe they have the value of pi correct and 1000s of years of mathematicians since them all have it wrong?

[Robust]

No he does not. OTOH, The Egyptians believed the universe and all events that occurred within it were governed by the will of gods. After death, the Egyptians looked forward to continuing their daily lives as an invisible spirit among their descendents on Earth in Egypt, enjoying all the pleasures of life with none of its pain or hardships. This vision is vividly depicted in the sculptures, reliefs, and wall paintings of Egyptian tombs, with the deceased portrayed in the way he or she wished to remain forever, accompanied by images of family and servants. The ancient Egyptians believed that the king was given divine power by the gods to maintain universal order and justice against the forces of chaos and evil. On the strength of his divine nature the king mediated between the gods and humankind. The ancient Egyptians believed in curses and spells. Do you believe this too since you seem to believe they have the value of pi correct and 1000s of years of mathematicians since them all have it wrong?

 

The Egyptians did not give us the original pi value we have - it was the Babylonians. As shown, and the Base 10 number system as well. I doubt that the ancient Egyptians had any great mental abilities.

[Rincewind]

OK then, Clay, here's a go at it. For the sake of simplicity, let's consider the circle with a radius of 2.25 and configure using the irrational pi and that of the oldest pi value on record, that of 256/81.

 

1. Irrational Pi: r^2*pi = 15.9043 ad infinitum area;

2. 256/81 Pi: r^2*pi = 16 area finite.

 

It's not just my opinion, Clay....just pure mathematics.

1. is correct to four decimal places;

2. is correct to no decimal places, and a very crude and inaccurate approximation that may have limited uses for some purposes not requiring a very high degree of accuracy.

 

What's the point you're trying to make here, Robust?

 

Can you provide a reference to that record of 256/81 that you speak of?

[C1ay]

Can you provide a reference to that record of 256/81 that you speak of?

According to this record the Babylonians used 3.125 = 3 + 1/8 and the Egyptians used 3.16045 = 256/81. Both are dated 2000 BCE. Perhaps he has a different reference for us.

[Robust]

According to this record the Babylonians used 3.125 = 3 + 1/8 and the Egyptians used 3.16045 = 256/81. Both are dated 2000 BCE. Perhaps he has a different reference for us.

The oldest reference we have dates to 5000BC - an archeologic engraving in stone giving the ratio of 256/81 - Babylonian. My investigative study gives a finite pi value of 3.1640625. The book is not closed on it yet, but I'm inclined to go with the finite value ....with all due respect.

[C1ay]

The oldest reference we have dates to 5000BC - an archeologic engraving in stone giving the ratio of 256/81 - Babylonian. My investigative study gives a finite pi value of 3.1640625. The book is not closed on it yet, but I'm inclined to go with the finite value ....with all due respect.

So post your reference and post your study as your proof. Thousands of mathematical minds over thousands of years have come to quite a different conclusion than you and you have yet to post anything that would even qualify as a mathematical proof in a high school classroom.

[Rincewind]

The oldest reference we have dates to 5000BC - an archeologic engraving in stone giving the ratio of 256/81 - Babylonian.

Nice. Where and what is this archaeological engraving? Be specific, please.

 

My investigative study gives a finite pi value of 3.1640625. The book is not closed on it yet, but I'm inclined to go with the finite value ....with all due respect.

Why would you be happy to go with a value that's at 20% variance to the correct value at only the second decimal place when there are values that are accurate to hundreds of decimal places? Any calculation that you make using this dodgy value for pi is going to be out by almost ¾%. Maybe whatever you're doing doesn't require any greater accuracy.

[maddog]

Well enough Clay. Let's leave off the "nitpicking" then and cut to the chase - which you seem to want to avoid. Would you agree then that the area to any closed continuum must be described by a whole number or endeing decimal?

Robust,

 

To answer you completely, accurately, and succintly is ABSOLUTELY NO!!! N--O-- MEANS NO!!

As you said earlier your not to up on math. PI is one of those constants in which as a number is

approximated and not exact. I have done this for you.

 

Let A = Area of circle, C = Circumfrence of same circle

 

A = PI * r^2 , C = 2 * PI * r where r = Radius of said circle

 

substituting our r so that it is irrelevant and solving for PI is as follows

 

A = PI * r^2 = PI * (C / 2* PI)^2 = C^2 / 4 * PI

 

Solving for PI

 

PI = C^2 / 4 * A

 

Were you to know Circumfrence and simultaneously the Area of the same circle EXACT, you would

be able to calculate PI EXACTLY! Since PI is a Trancendental Number, so to be EXACT would need

infinite precision (infinite number of digits). Something you are forgetting any Trancedental number

times a constant value is another Trancedental number and suffers the same consequences!

Thus you can only get an approximation with approximate measurements. :) :)

 

So, to sad, your series of formulas are fruitless, worthless, completely WRONG! :) :)

 

Maddog

[Qfwfq]

If you will, and considering that the circle is a closed continuum, using your irrational pi give the area to any circle as defined by a whole number or ending decimal. It can be done, but I seriously doubt that you can do it using the irrational pi.

What's the buzz?

 

If for example the radius is 1 divided by the root of pi the area will be exactly 1. If the radius is any rational divided by pi the area will be rational.

 

Would you agree then that the area to any closed continuum must be described by a whole number or endeing decimal?.

Why must it be? Here's an example not involving pi:

 

Consider the three lines: the x axis, the vertical line at x = 1/2, the curve given by the positive square root of x > 0. There is a closed figure encompassed by them and its area is the integral from 0 to 1/2 in dx of the positive root of x. This integral is equal to 1 over twice root 2. Is that a rational value of area?

 

edit: This integral is equal to 1 over thrice root 2.

 

If you can prove the square root of 2 is rational, I'll swim from the Bering strait to Antarctica.

[Robust]

What's the buzz?

 

If for example the radius is 1 divided by the root of pi the area will be exactly 1. If the radius is any rational divided by pi the area will be rational.

 

Why must it be? Here's an example not involving pi:

 

Consider the three lines: the x axis, the vertical line at x = 1/2, the curve given by the positive square root of x > 0. There is a closed figure encompassed by them and its area is the integral from 0 to 1/2 in dx of the positive root of x. This integral is equal to 1 over twice root 2. Is that a rational value of area?

 

If you can prove the square root of 2 is rational, I'll swim from the Bering strait to Antarctica.

We're not on the same page here - root 2 rules in my book and is an irrational number, as are all numbers not whole or with ending decimal, as are all pi values but for the recently given finite pi. When I say "irrational pi" I refer to the Euler & Company algorythmic decimal expansion - which y'all claim to be sacrosanct. It is not, as clearly shown.

[tom]

Clearly shown? Where ?